Asensio fired his side ahead moments before halftime from outside the box following a quick break, opening his account for his new club following a close-season transfer from Real Madrid.
PSG were not at their best but never looked troubled as Mbappe doubled the advantage in the second half when he rocketed a 20-metre shot into the back of the net.
The France forward scored again late on for his third goal in two Ligue 1 games, an impressive start to the campaign despite being frozen out of the squad for weeks in pre-season amid an ongoing contract stand-off.
Lens grabbed a consolation goal when Morgan Guilavogui scored with virtually the last kick of the game.
PSG move up to fourth in the table with five points from three games, while Lens, who finished second last season, one point behind PSG, have started the new campaign with only a draw from their opening three games.
Marseille eased to a 2-0 victory at home to Brest, ending the visitors’ 100% start to the Ligue 1 season.
It was a gritty performance and enough for three points as Chancel Mbemba headed in a free-kick inside four minutes.
Home defender Jonathan Clauss cleared off the line from Jeremy Le Douaron after that, before Marseille doubled their advantage midway through the second period.
Ismaila Sarr scored his first goal for the club following his move from Watford, turning in the rebound after Brest goalkeeper Marco Bizot spilled a cross.
Marseille move up to second place, level on seven points with leaders AS Monaco. Brest won their opening two games of the season for the first time in their history and remain third.
(Reporting by Nick Said; Editing by Ken Ferris)